# MxGPS: Multiplex Graph Transformers for a Power Grid Foundation Model

arXiv: https://arxiv.org/abs/2607.13763 · HTML: https://mlsanity.com/paper/2607.13763/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Attending to Graph Transformers](https://mlsanity.com/paper/2302.04181/) (2023)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Graph Mixture of Experts: Learning on Large-Scale Graphs with Explicit Diversity Modeling](https://mlsanity.com/paper/2304.02806/) (2023)
- [A Review of Graph Neural Networks and Their Applications in Power Systems](https://mlsanity.com/paper/2101.10025/) (2021)
- [Foundation Models for the Electric Power Grid](https://mlsanity.com/paper/2407.09434/) (2024)
- [DeepOPF+: A Deep Neural Network Approach for DC Optimal Power Flow for Ensuring Feasibility](https://mlsanity.com/paper/2009.03147/) (2020)
- [SafePowerGraph: Safety-aware Evaluation of Graph Neural Networks for Transmission Power Grids](https://mlsanity.com/paper/2407.12421/) (2024)
- [gridfm-datakit-v1: A Python Library for Scalable and Realistic Power Flow and Optimal Power Flow Data Generation](https://mlsanity.com/paper/2512.14658/) (2025)
- [Mind the Links: Cross-Layer Attention for Link Prediction in Multiplex Networks](https://mlsanity.com/paper/2509.23409/) (2025)
- [MoE-GraphSAGE-Based Integrated Evaluation of Transient Rotor Angle and Voltage Stability in Power Systems](https://mlsanity.com/paper/2511.08610/) (2025)

## Built on by (most cited first, 1 of 1)

- [Mycelium: A Generalizable Cross-Grid Multi-Task Model for Electrical Distribution Systems](https://mlsanity.com/paper/2609.33120/) (2026)

## Abstract (arXiv)

Single-task fine-tuning of graph neural networks (GNNs) for power grid problems exhibits a systematic failure mode: models that achieve the lowest in-distribution error degrade the most under topology shift. We term this topology overfitting: the tendency of task-specific gradient signals to encode relational structure particular to the training topologies rather than the underlying physics, causing models to fail on unseen grids despite strong in-distribution performance. To expose and address this failure mode, we introduce MxGPS (Multiplex GPS), a multiplex graph transformer that runs K task-specialised GPS branches over a shared node encoder, jointly trained on Static State Estimation (SSE) and AC Power Flow (PF) via a self-supervised pre-training and multi-task fine-tuning protocol, with a cross-branch attention module evaluated in ablation. The joint SSE+PF objective forces the shared encoder to simultaneously satisfy complementary gradient signals, preventing it from overfitting to topology-specific relational structure. Under a 3-fold sliding-window cross-validation spanning four unseen topologies (14-, 24-, 162-, and 300-bus), MxGPS attains 0% boundary violation rate (BVR) on all four zero-shot Power Flow topologies. Critically, models with substantially lower in-distribution PF error degrade by 190% to 1400% under topology shift, whereas MxGPS degrades by only 39%, an inversion that directly implicates topology overfitting as the failure mechanism rather than insufficient model capacity. With only 1.6M parameters (12x fewer than the GridFM reference baseline), MxGPS demonstrates that multi-task joint training is a principled and parameter-efficient mechanism for topology-agnostic generalisation in power grid foundation models.